-4(u+1)6u=2(u+2)-8

Solution for -4(u+1)6u=2(u+2)-8 equation:

-4(u+1)6u=2(u+2)-8

We move all terms to the left:

-4(u+1)6u-(2(u+2)-8)=0

We multiply parentheses

-24u^2-24u-(2(u+2)-8)=0


We calculate terms in parentheses: -(2(u+2)-8), so:

2(u+2)-8

We multiply parentheses

2u+4-8

We add all the numbers together, and all the variables

2u-4

Back to the equation:

-(2u-4)


We get rid of parentheses

-24u^2-24u-2u+4=0

We add all the numbers together, and all the variables

-24u^2-26u+4=0

a = -24; b = -26; c = +4;
Δ = b2-4ac
Δ = -262-4·(-24)·4
Δ = 1060
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{265}}{2*-24}=\frac{26-2\sqrt{265}}{-48}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{265}}{2*-24}=\frac{26+2\sqrt{265}}{-48}
$